Partial Differential Equations and Spectral Theory

Dipl.-Kaufmann Michael Demuth ist Geschäftsführer der Vermögensberatungsgesellschaft Creative Capital GmbH.

Bert-Wolfgang Schulze ist emeritierter Professor am Institut für Mathematik an der Universität Potsdam, Deutschland. Vor der politischen Wende war er Professor am Karl-Weierstrass-Institut in Berlin, 1984 Euler-Medaille der Akademie der Wisenschaften in Berlin. 1992-96 war er Leiter der Max-Planck-Arbeitsgruppe 'Partielle Differentialgleichungen und Komplexe Analysis' in Potsdam. Nach anfänglichem Studium in Geophysik erhielt er sein Universitätsdiplom in Mathematik in Leipzig 1968. Die Promotion zum Dr. rer.nat. 1970 und die Habilitation in Mathematik 1974 erfolgten an der Universität Rostock. Seine wissenschaftlichen Aktivitäten umfassen Potentialtheorie, Randwert-Probleme, pseudo-differentielle Algebren und Index-Theorie auf berandeten Mannigfaltgikeiten und Räumen mit Singularitäten, darunterTransmissions- und Riss Probleme, Asymptotik von Lösungen, Randwert-Theorie mit globalen Projektionsbedingungen.

Instability in the Spectral and the Fredholm Properties of an Infinite Dimensional Dirac Operator on the Abstract Boson-Fermion Fock Space.- Well-Posedness of Nonlinear Parabolic Equations of Viscous Hamilton-Jacobi Type.- Non-Convex Minimization - the Case of Vector Fields.- On the One Dimensional Behaviour of Atoms in Intense Homogeneous Magnetic Fields.- Semi-Classical Resolvent Estimates and Spectral Asymptotics for Trapping Perturbations.- Semiclassical Pseudodifferential Operators with Double Discontinuous Symbols and their Application to Problems of Quantum Statistical Physics.- A Free Boundary Value Problem Arisen in Unsteady Compressible Flow.- Some New Results on the Nonlinear Singular Partial Differential Equations.- A Unified Approach to the Theory of Fundamental Solutions, Non-degenerate Case.- Fourier Integral Operators in SG Classes: Classical Operators.- A Semigroup Criterion for the Completeness of Scattering Systems.- Parameter-Elliptic Boundary Value Problems and their Formal Asymptotic Solutions.- Solutions of q-Deformed Equations with Quantum Conformal Symmetry.- On the Regularization and Stabilization of Approximation Schemes for C0-Semigroups.- Pseudodifferential Operators with Symbols in Weighted Function Spaces of Quasi-Subadditive Type.- Spectral Analysis of Quantum Field Models with a Particle Number Cutoff.- On the Norm Convergence of the Trotter-Kato Product Formula with Error Bound.- Nonperturbative Techniques in the Investigation of the Spectral Properties of Many-Channel Systems.- Essential Self-Adjointness of n-Dimensional Dirac Operators with a Variable Mass Term.- Towards the Spectral Analysis of Schrödinger Operator with Fractal Perturbation.- On$$mathcal{H}_{ - 4} -$$-4-Perturbations of Self-Adjoint Operators.- GlobalAttractor for Generalized 2D Ginzburg-Landau Equation.- Local Asymptotic Properties of Multifractional Brownian Motion.- Strong Uniqueness for Dirichlet Operators with Singular Potentials.- Hardy Type Inequalities, Mourre Estimate and A-priori Decay for Eigenfunctions.- Surgery and the Relative Index in Elliptic Theory.- Propagation of Wave Packets and its Applications.- Gevrey and Analytic Properties of the Solutions of Several Classes of Partial Differential Equations.- Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps.- Stability of Inverse Operators of Boundary Value Problems in Non-Smooth Expanding Domains.- Local Algebra of a Non-Symmetric Corner.- The Integrated Density of States for a Random Schrödinger Operator in Strong Magnetic Fields. II. Asymptotics near Higher Landau Levels.- Partial Differential Operators with Multiple Symplectic Characteristics.- On the Homotopy Classification of Elliptic Boundary Value Problems.- Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula.- Eigenfunction Expansions Associated with Relativistic Schrödinger Operators.- The Time-Dependent Approach to Inverse Scattering.- Cone Conormal Asymptotics.- List of Participants.- List of Talks.

From the reviews:

"This present volume contains six expository articles in the area of partial differential equations and spectral theory. ... All articles are written by leading experts and give an overview of current developments to a broader audience. ... the volume should also be accessible to doctoral students in this area." (G. Teschl, Monatshefte für Mathematik, Vol. 164 (4), December, 2011)